Fig. 9. Basic configuration of narrow-band ANC system.
algorithm have never been proven formally. A modified
leaky version of the simplified hyperstable adaptive re-
cursive filter (SHARF) algorithm [52] has been developed
for ANC applications to improve the stability of the IIR
adaptive filter [53]. In that algorithm, a lowpass filter is
used to smooth the error signal for the filtered-U recursive
LMS algorithm, thereby providing a higher stability margin.
III. N
ARROWBAND FEEDFORWARD ANC
Many noises are periodic, such as those generated by
engines, compressors, motors, fans, and propellers. Direct
observation of the mechanical motion of such sources
generally is possible by using an appropriate sensor, which
provides an electrical reference signal that contains the
fundamental frequency and all the harmonics of the primary
noise. However, this technique is only effective for periodic
noise because the fundamental driving frequency is the only
reference information available.
A. Introduction
A basic block diagram of narrow-band ANC for reducing
periodic acoustic noise in a duct is illustrated in Fig. 9. This
system controls harmonic sources by adaptively filtering a
synthesized reference signal
internally generated by
the ANC system. This technique has the following advan-
tages: 1) undesired acoustic feedback from the canceling
loudspeaker back to the reference microphone is avoided;
2) nonlinearities and aging problems associated with the
reference microphone are avoided; 3) the periodicity of the
noise removes the causality constraint; 4) the use of an
internally generated reference signal results in the ability
to control each harmonic independently; and 5) it is only
necessary to model the acoustic plant transfer function over
frequencies in the vicinity of the harmonic tones; thus, an
FIR filter with substantially lower order may be used.
The reference signal generator is triggered by a syn-
chronization pulse from a nonacoustic sensor, such as a
tachometer signal from an automotive engine. In general,
two types of reference signals are commonly used in
narrow-band ANC systems: 1) an impulse train with a
period equal to the inverse of the fundamental frequency
of the periodic noise [54] and 2) sinewaves that have the
same frequencies as the corresponding harmonic tones to
be canceled. The first technique is called the waveform
synthesis method, which was proposed by Chaplin [55].
The second technique embodies the adaptive notch filter,
which was originally developed for the cancellation of tonal
interference [56] and applied to periodic ANC [57].
The waveform synthesis method discussed next in
Section III-B employs synchronous sampling. However,
for some applications, the actual period will vary from
the nominal value as a function of loading conditions.
Therefore, it is sometimes desirable to operate asynchro-
nously with a fixed sampling rate so that the secondary-path
estimate filter coefficients do not have to be changed as
a function of actual machine rotation rate. Also, some
digital signal processors cannot be efficiently utilized on
a synchronous signal-driven basis. Asynchronous ANC
systems using the FXLMS algorithm eliminate the problem
of having to change
as the sampling rate varies and
are implicit in the later formulations of Sections III-C and
III-D.
B. Waveform Synthesis Method
1) Structures and Algorithms: The waveform synthesizer
[55] stores canceling noise waveform samples
in unique contiguous memory addresses,
where
is the number of samples over one cycle of the
waveform and
is the current time index. These samples
represent the required waveform to be generated and are
sequentially sent to a D/A converter to produce the actual
canceling noise waveform for the secondary loudspeaker.
Thus
(19)
represents the
th element of waveform samples, where
mod and can be implemented as a pointer
incremented in a circular fashion between zero and
for each sampling period, controlled by interrupts generated
from the synchronization signal.
The residual noise picked up by the error microphone
is synchronously sampled with the reference signal timing
pulses. In a practical system, there is a delay between the
time the signal
is fed to the loudspeaker
and the time it is received at the error microphone. This
delay can be accommodated by subtracting a time offset
from the circular pointer
Thus, the adaptation unit
adjusts the values of the waveform samples using a variant
of the LMS algorithm
otherwise
(20)
where
and is the time delay, which is
constant for a given loudspeaker-microphone arrangement,
is the sampling period, and greatest integer less
than or equal to
This offset number must be updated
as the sampling rate varies, since it is synchronized with
the noise source.
KUO AND MORGAN: ACTIVE NOISE CONTROL 949
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